{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loadDataSet(filename):\n",
    "    '''\n",
    "    加载数据\n",
    "    Args:\n",
    "        filename: 文件名\n",
    "    Return:\n",
    "        特征值矩阵，预测值矩阵\n",
    "    '''\n",
    "    dataArr = []\n",
    "    labelArr = []\n",
    "    with open(filename) as fr: \n",
    "        for idx,line in enumerate(fr):\n",
    "            lineArr = line.strip().split('\\t')\n",
    "            if idx == 0:\n",
    "                numFeat = len(lineArr) - 1      # 减1是因为最后一个是预测值\n",
    "            lineArr = list(map(float, lineArr))\n",
    "            dataArr.append(lineArr[:-1])\n",
    "            labelArr.append([lineArr[-1]])\n",
    "    return np.mat(dataArr),np.mat(labelArr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 最小二乘法计算参数\n",
    "$$ w = (X^T X)^{-1}X^Ty $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def standRegres(xMat, yMat):\n",
    "    '''最小二乘法,计算最佳拟合直线'''\n",
    "    xTx = xMat.T * xMat\n",
    "    # 如果矩阵行列式为0，则无逆\n",
    "    if np.linalg.det(xTx) == 0.0:\n",
    "        print(\"This matrix is singular, cannot do inverse\")\n",
    "        return\n",
    "    ws = xTx.I * xMat.T * yMat\n",
    "    return ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1.      , 0.067732],\n",
       "        [1.      , 0.42781 ]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xMat, yMat = loadDataSet('ex0.txt')\n",
    "xMat[0:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 2) (2, 200) (200, 1)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "matrix([[3.00774324],\n",
       "        [1.69532264]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ws = standRegres(xMat, yMat)\n",
    "ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[3.12257084],\n",
       "        [3.73301922],\n",
       "        [4.69582855],\n",
       "        [4.25946098],\n",
       "        [4.67099547],\n",
       "        [3.89977285],\n",
       "        [3.65007895],\n",
       "        [3.06514517],\n",
       "        [3.23286683],\n",
       "        [3.24221654],\n",
       "        [3.42785945],\n",
       "        [4.10677005],\n",
       "        [4.24737842],\n",
       "        [3.40925159],\n",
       "        [4.6518468 ],\n",
       "        [4.03763819],\n",
       "        [3.61572324],\n",
       "        [3.25838991],\n",
       "        [4.08905393],\n",
       "        [3.39829811],\n",
       "        [3.12681762],\n",
       "        [3.12159094],\n",
       "        [4.57689489],\n",
       "        [4.22453225],\n",
       "        [3.03380205],\n",
       "        [3.575795  ],\n",
       "        [3.07638008],\n",
       "        [3.36812645],\n",
       "        [4.05412689],\n",
       "        [3.92524508],\n",
       "        [3.08463121],\n",
       "        [3.22264573],\n",
       "        [3.95116656],\n",
       "        [4.53547307],\n",
       "        [4.63266931],\n",
       "        [3.47321272],\n",
       "        [3.67637171],\n",
       "        [4.48687834],\n",
       "        [3.70271024],\n",
       "        [4.54873897],\n",
       "        [3.29055527],\n",
       "        [4.13515992],\n",
       "        [3.4548456 ],\n",
       "        [3.39972557],\n",
       "        [3.9451346 ],\n",
       "        [3.08868473],\n",
       "        [3.62780072],\n",
       "        [3.84693134],\n",
       "        [3.84432733],\n",
       "        [4.35061   ],\n",
       "        [4.31256527],\n",
       "        [3.43466109],\n",
       "        [3.31620889],\n",
       "        [4.37786401],\n",
       "        [3.57417766],\n",
       "        [3.58183035],\n",
       "        [3.77501915],\n",
       "        [4.18560255],\n",
       "        [4.00951278],\n",
       "        [3.52978055],\n",
       "        [3.25926809],\n",
       "        [4.1981649 ],\n",
       "        [4.23099312],\n",
       "        [4.13833018],\n",
       "        [3.2195416 ],\n",
       "        [4.0559375 ],\n",
       "        [3.65380697],\n",
       "        [3.66153255],\n",
       "        [4.32530562],\n",
       "        [3.20455155],\n",
       "        [3.20353097],\n",
       "        [4.13260677],\n",
       "        [3.43985386],\n",
       "        [4.69270407],\n",
       "        [3.50859919],\n",
       "        [4.62257705],\n",
       "        [3.52828697],\n",
       "        [3.47779009],\n",
       "        [3.48090949],\n",
       "        [3.30565212],\n",
       "        [3.27286288],\n",
       "        [4.25069447],\n",
       "        [4.44561758],\n",
       "        [4.31514894],\n",
       "        [3.73587075],\n",
       "        [3.28268389],\n",
       "        [4.56246261],\n",
       "        [3.54184447],\n",
       "        [3.34930498],\n",
       "        [3.51131849],\n",
       "        [3.57846852],\n",
       "        [4.13701291],\n",
       "        [3.99762179],\n",
       "        [3.15189822],\n",
       "        [4.17244007],\n",
       "        [4.61771487],\n",
       "        [3.32970536],\n",
       "        [4.43864133],\n",
       "        [3.57277394],\n",
       "        [3.73170535],\n",
       "        [3.79838917],\n",
       "        [3.94128791],\n",
       "        [3.47940404],\n",
       "        [4.56535313],\n",
       "        [4.51074001],\n",
       "        [3.97320914],\n",
       "        [3.12027706],\n",
       "        [3.57694952],\n",
       "        [3.73141375],\n",
       "        [3.6786604 ],\n",
       "        [4.18467182],\n",
       "        [3.47015945],\n",
       "        [3.86132972],\n",
       "        [3.1215316 ],\n",
       "        [3.07271818],\n",
       "        [4.02344833],\n",
       "        [4.61330533],\n",
       "        [4.14577773],\n",
       "        [3.74488818],\n",
       "        [3.87130839],\n",
       "        [4.27828923],\n",
       "        [3.10609569],\n",
       "        [3.82654678],\n",
       "        [3.79907916],\n",
       "        [3.61427374],\n",
       "        [4.61681295],\n",
       "        [3.71523529],\n",
       "        [4.56822162],\n",
       "        [3.27294765],\n",
       "        [4.1209972 ],\n",
       "        [4.05277064],\n",
       "        [4.45457905],\n",
       "        [3.23372127],\n",
       "        [4.1826137 ],\n",
       "        [3.31027187],\n",
       "        [3.34600419],\n",
       "        [3.13188155],\n",
       "        [3.49347861],\n",
       "        [3.31633604],\n",
       "        [4.06142526],\n",
       "        [3.5919243 ],\n",
       "        [3.68342425],\n",
       "        [3.82212368],\n",
       "        [3.26772097],\n",
       "        [3.29907766],\n",
       "        [4.47772699],\n",
       "        [3.38724969],\n",
       "        [3.90338389],\n",
       "        [4.5169059 ],\n",
       "        [3.1880442 ],\n",
       "        [4.56385616],\n",
       "        [3.03292726],\n",
       "        [3.97014739],\n",
       "        [3.12447299],\n",
       "        [4.03092979],\n",
       "        [3.90973965],\n",
       "        [4.11201199],\n",
       "        [4.53561039],\n",
       "        [3.35416039],\n",
       "        [4.18782512],\n",
       "        [4.64190543],\n",
       "        [4.67151593],\n",
       "        [4.68257113],\n",
       "        [4.68771813],\n",
       "        [4.25553631],\n",
       "        [3.43763299],\n",
       "        [4.15161473],\n",
       "        [4.60027508],\n",
       "        [3.4068544 ],\n",
       "        [3.195112  ],\n",
       "        [3.37736257],\n",
       "        [4.48229758],\n",
       "        [3.3414336 ],\n",
       "        [4.6321641 ],\n",
       "        [4.6567378 ],\n",
       "        [4.27210978],\n",
       "        [3.76330447],\n",
       "        [3.80548918],\n",
       "        [3.93887547],\n",
       "        [3.5768478 ],\n",
       "        [4.5076613 ],\n",
       "        [4.56560234],\n",
       "        [3.75676222],\n",
       "        [3.20541447],\n",
       "        [3.61682859],\n",
       "        [4.38911078],\n",
       "        [3.66404502],\n",
       "        [4.67296204],\n",
       "        [4.33158679],\n",
       "        [4.11405146],\n",
       "        [4.4827248 ],\n",
       "        [4.03299809],\n",
       "        [3.44040992],\n",
       "        [4.24625442],\n",
       "        [3.84494273],\n",
       "        [3.44346998],\n",
       "        [4.42119307],\n",
       "        [3.12657688],\n",
       "        [3.90129695],\n",
       "        [3.20467701]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yHat = xMat * ws\n",
    "yHat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x153fa696390>]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x153fa601a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.scatter(xMat[:, 1].flatten().A[0], yMat.T.flatten().A[0])\n",
    "yHat = xMat * ws\n",
    "ax.plot(xMat[:,1].flatten().A[0], yHat.T.flatten().A[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 计算预测值与实际值的相关系数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.98647356],\n",
       "       [0.98647356, 1.        ]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(yHat.T, yMat.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 局部加权线性回归（LWLR）\n",
    "给待预测点附近的每个点赋予一定的权重，在子集上基于最小均方误差进行普通的回归，这种算法每次预测均需要事先选取出对应的数据子集。回归系数计算如下：\n",
    "$$ w = (X^TWX)^{-1}X^TWy $$\n",
    "其中 $ W $ 是权值矩阵（对角）<br/>\n",
    "使用“核”来对附近的点赋予更高的权重：\n",
    "$$ W(i,i) = exp(\\frac{|x^{(i)}-x|}{-2k^2}) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lwlr(testPoint, xMat, yMat, k=1.0):\n",
    "    '''\n",
    "    给定空间中一点testPoint,计算出对应的预测值\n",
    "    '''\n",
    "    m = np.shape(xMat)[0]\n",
    "    weights = np.mat(np.eye((m)))\n",
    "    # 权重值大小以指数级衰减;为每个样本点计算权重\n",
    "    for j in range(m):                      \n",
    "        diffMat = testPoint - xMat[j,:]     \n",
    "        weights[j,j] = np.exp(diffMat*diffMat.T/(-2.0*k**2))\n",
    "    xTx = xMat.T * (weights * xMat)\n",
    "    if np.linalg.det(xTx) == 0.0:\n",
    "        print(\"This matrix is singular, cannot do inverse\")\n",
    "        return\n",
    "    ws = xTx.I * (xMat.T * (weights * yMat))\n",
    "    return testPoint * ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lwlrTest(testMat,xMt,yMat,k=1.0):  #loops over all the data points and applies lwlr to each one\n",
    "    '''计算整个训练集的预测值，可用于画图选择k'''\n",
    "    m = np.shape(testMat)[0]\n",
    "    yHat = np.zeros((m,1))\n",
    "    for i in range(m):\n",
    "        yHat[i] = lwlr(testMat[i],xMat,yMat,k)\n",
    "    return yHat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[3.176513]])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xMat, yMat = loadDataSet('ex0.txt')\n",
    "yMat[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[3.12204471]])"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lwlr(xMat[0], xMat, yMat, 1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "def showLwlrPlot(xMat, yMat, k=1.0):\n",
    "    yHat = lwlrTest(xMat, xMat, yMat, k)\n",
    "    srtInd = xMat[:, 1].argsort(0)\n",
    "    xSort = xMat[srtInd][:, 0, :]\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)\n",
    "    ax.plot(xSort[:, 1].T.flatten().A[0], yHat[srtInd].T.flatten())\n",
    "    ax.scatter(xMat[:,1].flatten().A[0], yMat.T.flatten().A[0], s=2, c='red')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x153fa66acc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "showLwlrPlot(xMat, yMat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x153fa6bae10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "showLwlrPlot(xMat, yMat, 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TnctTP27mxbgz9E+I4Ys/P9DEXo7s/s6KiDsQAxw2xtxYaNuTwP1ALpAE3GeM2e/IQJVS9ok/lsb2wOa8vPpr7jq1DbZvt5ZGCtezw8NpEBHBEN8sfsuoyXMtBU/38/29YZ++xrDFi637Toy01tVv+iecPAlnT1xwV+uNXYLp2jSA8bM2MX7WJlac2sGQPSms65qLn7cHc2IP8ueOY+xOSmdCex8e3RSNe/glLsSqMpP8WlqJDa0JPBSoXUxyHwBEG2POiMhDQH9jzB2XOl5oaKiJidGV+JRypDPZuYz+NJr4xNOsenYggVs2WC9mhodf9GLlwRG3s/TQGe6qn4sUnIYgKur8vgA33WRN7PXqwfz5xR4vN8/C+3/t5oM/d2GAujWEKaO68uiMjQTmnOG//RrQZ0Tfcjjz6kNEYo0xJa9RbYwp8QtoAvwJDAQWlNC2G7C6pGN2797dKKUcJ2fVanPfgx+YFs8uMIu3HrV/xzVrjBkyxPrvxQwZYgwYU6/epdvZRG49apo/u8B8v3a/ycuzmB9HjzeJvnWtx1FlgnV50xLztr1lmfeAiYBfSQ2BscAiO4+rlHKQj6Yv5M9GYfzn4FKu7zjc/h3tWeUov/d+ib8AChrSsSGbJg8moGYNAG577A44tVPHsVegEi+oisiNwHFjTKwdbcdgLd28dZHt40QkRkRikpKSSh2sUqp4Wbl5fB3SmwGp+xjTr63jp/LN/wAoxTj0/MR+ufursrFntEwfYISI7ANmAQNF5LvCjURkEPA8MMIYk1XcgYwx040xocaY0KCgoDKErZQqKHJrIieyDPc8cRvMnXvRG4cqVCWbL766KbEsY4yZBEwCEJH+wNPGmDEF24hIN+ATYKgx5ng5xKmUuoRZv0QTkppM32W/XFhCcaZKNF98dXTZg0xFZArWwv48rGUYX2C2bRWVA8aYEY4JUSl1Kbl5Fjamw+hd0bjNngsnTlSOZFpZPmSqqVIld2PMMmCZ7fHkAq8PcmhUSim77U5KJ9PDiy7pifDqq84O5zx7LtSqcqO3hynl4uIO2Ra6mDcD6vs6ORpVWej0A0q5uLhDKfh6edAysJazQ1GViCZ3pVzclkOpdGpcGzfbfC9KgSZ3pVxaZk4eO46mcWWTgJIbq2pFk7tSLirPYnhi1iay8yz0++JtHU+uLqAXVJVyQcYYXvhlC5HbEnnx8Ap6//QFpB/W0SnqHE3uSrmgt3+PZ+a6gzwyoBVja9eFJF1/VF1Ik7tSLub3ucuZti6d0c29ePr6diCiPXZVhNbclXIxn/z1N82Tj/CfX9/Bdke4UkVoclfKhWw6mEKsbzD3ZuzSlYzUJWlZRikX8vmqvfh5eXDb56+Crj+qLkF77kq5iCMpZ1m45Sh39miKryZ2VQJN7kq5iK+j9mGM4Z7eIc4ORbkATe5KuYAz2bnMjD7ADZ0a0aROTWeHo1yAJnelXMBPsYc4nZnLfdeEODsU5SLsTu4i4i4iG0VkQTHbvETkBxHZLSLRIhLiyCCVqs4sFsMXq/dxZdMArmpWx9nhKBdRmp77eGDHRbaNBZKNMa2BqcAbZQ1MqWrPtgbp0l9XsPdEBmOvaaHj2pXd7EruItIEGA58dpEmNwNf2x7PAa4T/S1Uqmxsa5B+/scOGvl7c0Onhs6OSLkQe8dTvQdMBPwusr0xcBDAGJMrIqlAPeBEmSNUqprKmzyZmfU6scavKc/1DsHTXS+RKfuV+NsiIjcCx40xsZdqVsxrpphjjRORGBGJSUpKKkWYSjlOTp6Fd7/8k1PDb6nU0+R+lZDFC00H0D79GKNJdHY4ysXY0xXoA4wQkX3ALGCgiHxXqM0hoCmAiHgA/sCpwgcyxkw3xoQaY0KDgoLKFLhSlyt2fzLvx2cyI9nLWvqohE6mZ/FN7BG6Hd7Jomlj8X/tZWeHpFxMicndGDPJGNPEGBMC3An8ZYwZU6jZPOAe2+NRtjZFeu5KVQbxiWkA/B46pFJOk7vrWBq3fLiaoz4BPHkiBunZs1LGqSq3yy7iicgUERlhe/o5UE9EdgNPAs85IjilysNOW3KPq9mAI1d0LbLdGMNL0/9gzugnMGvWVGhsa+atYOTbSzibkckPfWpzrUmGqVMhLKxC41Cur1QTVBhjlgHLbI8nF3g9E7jNkYEpVV7iE08T7O/NkdRM/thxjLvDQi7Yvvt4Ol8lZEHzwSz/OppXrrqa2t6e5R6XZc0aJi3aTVBuNt/u/IPG0emweLF1o87XrkpJL7+raiUrN4/4wykM2r2OVr5uLNl+rEibtXutl4vuSdrMwrptGf7+SjYeSD437ry8LsKunPoV+/0b8MTm+TT+91PWUsyQylk6UpWfJndVrURuTSQjDwb9NZvBe9YTteckqStWX5C0oxNO0qC2Fy99NokfHwzDYoHbPo7iw48WYFn8e7ldhI0ceDt+eVkMefd5axkmLMzaY9eSjLoMmtxVtfLd2v00r+XGNe3qc/2oAeRaDMs+/AGzeDFERGCMIXrvKXq2qIeI0L15XRaOv5YhHRvyZnBv3rj3pXLrSW9NyaXLmeN4uev9f6rsNLmraiM+MY31+5L5v75tcYuMpOsN1xDk58X4kCFc/eQPxD3+PHtPZJCUlkXPlnXP7efv48n//q8bfQI9WF67ebnElpNnIT45m47b11Xa4ZnKtWhyV9XGjOj91HB347bQpgC4uQmDrmgAwAnPWty1/ixfrdkHQM8W9S7YV0Tosm0te2r4kz2lbGPO0zJz2HUsjbiFK0kbdhNERbHrWDrZbu50bOCrNXblEJrcVbWQkZXL3A2HGda5IXVr1Tj3+vUdG5x77Ese30TtJ9DXi1ZBtYoco/2wfuS4e7Jn/CS73jM3z8Ij7y9h9aj7z9Xz9ySl0+eVJQyeuoIRK04zzj8MExHBtiOpAHR8/1WtsSuH0OSuqr6oKOb/ayJpWbmM6XVhWaV3K2sPvV9CDDOX/pfGPm5cvy8GWbu2yGE69Q8FICagmV1vuyDuKL8dyeavZIGICDJz8njk+w24nz3De/Pf5v6DUUQ1v5JVD/2bbUdO4+PpTovAoh8qSl0OTe6qyjMREXxXozntTh2k+5GdF2zz8nBnddR/+fCX12mWmcKKqPeJ+PKFYuveLQNr0TKoFou2HAWsPfONv63EFDM80hjDR8v2AHCsdQcIDydi/jZ2Jqbx7jVB3NLUi2ceGkbjAB/ePujGtiOpXNHID3c3vZiqHEOTu6ry4h5/nq0NW/PPmAXIlClFtjd+PYJaA/vB1Km4h0/Gc/CgYuveIsKNnRuxNuEkX6/Zx6B3l3PrytPMPpJX5MNgafxx4o+l4ekuHL+qF794N2PmuoM83L8VA27pB5GReF3Tm/GD2rD5UCrr9yXTMdi/3L4HqvrR5K6qvO/P1KamO9zaUIq/WFlwPHkJY8uHdwnGYiB83jZq5mbR2MeNWf3uKHLcj5btoXGAD9e1b8CuY2n8++ct9Aipy5OD217QbmS3xrS01fc7Btd2zAkrhSZ3VYXlWQxxh1L4MeYQN3dvit/C+WW+WNk2YQsvrfmWT3+awm/L3+PeAe3YUKsRu1p2Otdm/b5TrN+XzAPXtiA4wIfkMzn4eLrz/uhueBSak93D3Y2JIYK7sRCacqBMsSlVUKnmllGqstu5eCXTf1pHfIuO7M4wZOVaALjzavsugpZEpkzh3pWLoV49CJ/PrZ0b80bkTn5Yf5AXbuwAwMfL9lC3Vg3uuLoZP8xegRjD1C5eNPT3LvaYQz99jc1LV+C7uS9cr3PIKMfQ5K6qjMycPB6MPMDJmk246mACvYf3p00DPzoF+9PBUSWP/PJLeDiEhREIDO7QgLnr9jFx2tMkDB/Fn4ca8GR7H3xquHPnd29zzbo4Wm/uCDf3vegxfYnQ8e3KoTS5q6ohKorpHy9kX6NefLPnF/o+eR+EdXD8++TX5Au4/eqmLNqayB97T/PrqoPUauTH3bOnw70D8Z78Aq0jSkjcxRxTqbLSmruqEg68NpVpgd0YnryLvrM/PV9bL+eZHAH6tgmikbcbD98yicUhoTx4ajMBL9iWNNDJv5STaHJXVcJ7Qx7A3U144Y6rL9wQEWGdE70c52txdxPGXtcOgODsNMbeP0yTuXI6exbI9haRdSKyWUS2iUiR/yUi0kxElorIRhGJE5Fh5ROuUhTbG9+U6ck1nZvSaGCfC9tW0Jzo/+rTgq/2/Mrv0+6j5itFx9IrVdHsqblnAQONMeki4gmsEpFFxpiC92e/APxojPlIRDoAC4EQx4erFOd74wCRkWTm5LHvRAY3dm5UtG0F1bPdo9fS/2AcdOuiF0ZVpVBicrctdJ1ue+pp+yq8+LUB8ocj+ANHHBWgUkUUHLGCdVk8i4G2Df2cF1NEBERHW/9K0JKMqgTsGi0jIu5ALNAamGaMiS7U5CXgdxF5DKgFDLrIccYB4wCaNXPMuGNVDRXqjf99zLrgdXtnJvdCHzhKOZtdF1SNMXnGmK5AE6CHiHQq1GQ08JUxpgkwDPhWRIoc2xgz3RgTaowJDQoKKmvsqppbv2AFSTfeSvyGeGq4u9G8nhNnVNRRMaqSKdU4d2NMiogsA4YCWwtsGmt7DWNMlIh4A4HAcQfFqdQF/tp5jPtWpVGz7T+pvf0ErZoH4+mug7+UymfPaJkgEQmwPfbBWnLZWajZAeA6W5srAG8gybGhKmV1Ij2LiXPiaF/bnQEZh0is4UvnxjrpllIF2dNzbwR8bau7u2EdFbNARKYAMcaYecBTwKciMgHrxdV7bRdilXIoi8Xw9OzNnM7M5ftHr6Fdw6E8lZROPV8vZ4emVKViz2iZOKBbMa9PLvB4O9CncBulHG3R1kSWxScx5eaOtLNdQG25e4t1tIptvhellN6hqlyIMYbpCzfT/Owp/jlh9PmbmCrgLlSlXI0md+UyYvYnszklj7Erf8A9eu35ZF5Bd6Eq5Up0VkjlMj5dkUCAm4VRB9ZDhw7nk7nOqqhUEdpzVy5h74kMluw4xpgjsdQ8eRyaNtX6ulKXoD135RK+WLUXTzc37r5nMCSu1RKMUiXQ5K4qveSMbGbHHuSWbsHUH3AlDNASjFIl0bKMqvTe/GYFmTkW7vc77exQlHIZ2nNXldqM6APM3J/FQ1GzabspEYZor10pe2hyV5VW7G8rCF+eQr9aOTztc0zr7EqVgiZ3VSmt3n2CB5edoHHqSd7ftgD3yEXODkkpl6I1d1XpzN1wiHu+WEdwQE1mHo3EP3+xaaWU3bTnrioNYwwfLtvDW4vjCWtZj4/v6o6/z1Bnh6WUS9Keu6o0NhxI5q3F8dx8Kp6vO1rw9/F0dkhKuSztuatKY/PBVABe+P5lahzoqVMKKFUG2nNXbItcyaGbbjs/y6KT7Ew8TaCXEHRtTx0Zo1QZ2bMSk7eIrBORzSKyTUSKnVdVRG4Xke22NjMcH6pymKgoGDoUoqIwxnDf70eYWKub06fM3bn7KO1P7Nd52ZVyAHvKMlnAQGNMuoh4AqtEZJExZm1+AxFpA0wC+hhjkkWkfjnFqxwhf/5z4NCMuRyr4UtS884k/b9+OGvZ8tw8C/Gnsrh7RwxE/KolGaXKyJ6VmAyQbnvqafsqvITeA8A0Y0yybR9dGLsyyy95hIcTuz8ZAIu4EenThLucFNKepAyy3Dy4ooEvPK4lGaXKyq6au4i4i8gm4DiwxBgTXahJW6CtiKwWkbUiouPXKqn0rFye2O/Nxseeh4gINqzbQa0a7rQMrMXCuKNOi2vDAeuHzFUfvKolGaUcwK7kbozJM8Z0BZoAPUSkU6EmHkAboD8wGvhMRAIKH0dExolIjIjEJCUllS1yZZ8C9XWAD/7cxS+bjnDv0uOYxYuJ3XaQrs0CuPHKYKL3niQpLeuS+5eHPIvh26j9NK3rQ/N6NcvtfZSqTko1WsYYkwIsAwr3zA8Bvxpjcowxe4F4rMm+8P7TjTGhxpjQoCBnVXermQLri+4+ns4Xq/cCkOrhzZZBt7CjZn26N6vD8M6NsBiInL/mwmReAeuT/rThENuPnuaZDT8ja9eWvINSqkQl1txFJAjIMcakiIgPMAh4o1CzX7D22L8SkUCsZZoERwerLoOtvm4mTyZi/ja8PdyZsXP8HrcVAAAUr0lEQVQWt7UZxSct+2EBrmpeh7YNfGkVVIsX4zL4y68Xdb5cQ52T/rS651lGA1JOQxPPZOfy9uJ4umYkctMP/4OUXXoxVSkHsKfn3ghYKiJxwHqsNfcFIjJFREbY2iwGTorIdmAp8Iwx5mT5hKxKxba+6O/+LVm56wQTBrcl9KkHCMrJYFEd6x9X3ZrVQUQY3iUYgKWtrmZdkw58tWYf/958hsVvf2lXHXz5r8vZO+KO873+S5V0bNvef2cOx9OyeLGNO6KLXCvlMCUmd2NMnDGmmzGmizGmkzFmiu31ycaYebbHxhjzpDGmgzGmszFmVnkHruyTkJTO5F+38uSMWNqePcldchTp3Zue3VtjAdo28D13m/+wzg0BuKtXc1ZNvoH44QH452by+/KtF38DW5LOXLWGcatTuLfRINJfftW67RIlndyIKbyU25yPU/0YueVPus/42Npj14upSjmETj9QheXmWRj1cRTpWbkMT9rJ43PexTO+M0RG0otUFgDdvXPOtW/fsDZzrvGj07RnocELeLw8hQGenVhKL/IsBnc3KfomtgQe69uErNa3sr9OMC9fOd5atysw5LKw1//xNF/tyeS+hJX8e9F/ocfV5fI9UKq60ukHqrBdx9M5lZHNG//ozNR/9aZFj87nEu01sz7G3ZJH2PJfL9gn9H+v4h250Jq0w8MZVCuTZA+fc0MViwgPhyFDWH3DaDzchHvCmvPDgSwWb0s8VxIq3BvPzbMwN9HC8M6NmDzhZjyuHwxTp5bL90Cp6kqTexUWt3wDAF1P7CuSaEMmPcGynd9y0+OjL9zJlqzzpwDo+9VUPNyEP3YcK/5NbMddnelN16YBPD+8A50a1+a5n+LYdiSVT5bvITfPcsEuv246wqmMbG66stFFPwCUUmWjyb2qiooi5odFBJw9Tcg7/ym6PSyMpvNmI717F3m9YLKt7e1Jz5Z1+XNH0ZuO0zJzOJJyltSzOWw5lELv1oHU8HDjvTu6cTYnj+Hvr+K1RTv5acOhc/v8sf0Yz87ZTGj6EQak7HXoKSulztOaexVlIiJY0+J2eh77u8zDGK9r34ApC7azcMtRjqZmsuVQCnGHU0lIysDTksfkrn5YDPRpVQ+A1vV9eX7YFbz46zYA/rtwG7d0a0x0wike/n4DHdOP8eWn4/Ha3VeHPSpVTrTnXkVteux5Dvs3oN/Nfctc8hh0RQMAHv5+Ay8v2M7ahFO0DvLlX0mbyHFz560Np/DxdKdbszrn9hnTqzl3HV7PTduXc+SshUlztzDu2xha1ffl61Ht8BvQV4c9KlWOtOdeRX2XUZta7qcZ8e27EOJdpgTfrF5NpicswH1DLJ3bN6H+grkAWFpn8+0vJzjt4c3go9upsd7/3PuICC/vioToaE7Ub8zcDdDGz53vxvYgwNcL+mmPXanypD33Kig5I5v5cUe49UAMvosWwIQJxTcsxbwx10+4m+ta16X+88+ce82td2/GJqzEIy+Xx377qOh49qlTYcgQXtr7B7dsW8r3UdOp5+tVllNTStlJe+5VRVQUZ15+hZNPPces3ECycy2MORJ76X0KzOteYu07/0JrIc/98SkPZX1MQM5ZCP+m2H3aRUXxnm1opVKqYmhyd3VRURx4bSq3th7FyS4PwZJUIJUe6Ydpf8eN4Jl98aR6iZuM7CVvvknAv/8Nr75z8dLPRT4YlFLlR6xrcVS80NBQExMT45T3rkrM0KE85d6BeR37MyExmqBhgwmcO4uuC2ZSt68mVaWqGhGJNcaEltROe+4u7sPRE5m74yyP7F/FI4+PsPaSm3vB6X1aBlGqGtMLqi5s6+FU3tpxlptPxfPUrDfOX9CsyLs+K2AxD6VU6WnP3YXNiT1EDQ83pozpiduB653TUy/NRVmlVIXR5O6icvIszN98hMH1PfB/9eVzc8FUOAdclFVKOZ49KzF5AysAL1v7OcaYYv8ni8goYDZwtTFGr5aWoxV/J3EyI5tbt8x3bs9ZR8IoVSnZ03PPAgYaY9JFxBNYJSKLjDEXLHYpIn7A40B0OcSpCpm78TB1a9Wg3/i79eKpUqoIe1ZiMsaYdNtTT9tXceMnXwbeBDIdF54qTurZHJZsPcqIfevxdBOdMlcpVYRdo2VExF1ENgHHsa6hGl1oezegqTFmQTnEqAr5ePkesi1w+/zPil3CTiml7Eruxpg8Y0xXoAnQQ0Q65W8TETdgKvBUSccRkXEiEiMiMUlJSZcbc7V28NQZPl+1l5FNatDhqrZajlFKFatU49yNMSnAMmBogZf9gE7AMhHZB/QC5olIkTuojDHTjTGhxpjQoKCgyw66Onvr+9W4ZWfxdAcfLccopS6qxOQuIkEiEmB77AMMAnbmbzfGpBpjAo0xIcaYEGAtMEJHyzjevM1HmHc4m3FRswl+s5jVlZRSysae0TKNgK9FxB3rh8GPxpgFIjIFiDHGzCvXCBUAfy9eyXN/nCC0puFR32SYrOUYpdTFlZjcjTFxQLdiXp98kfb9yx6WKsgYwzML/qYmXkzb8TM1Fi10dkhKqUpO55ZxAUu2H2NzrYZMPBlLg+efdnY4SikXoNMPVHIWi+Gd3/+mZWAtRr7yDrjr57FSqmSaKSq5+T8tJ/5YGk80Bw9N7EopO2m2qMRy8ixMXXOY9sf3cuPnrzs7HKWUC9HkXomt3JXEPq8AnsjYgZverKSUKgWtuVdiS3cm4ePpzoDv3wcPd2eHo5RyIdpzr6TMmjUsWx5H77pueGliV0qVkib3SirmnU856OXPgJjfnR2KUsoFaXKvhLJy8wgPvYP6OemMfHCks8NRSrkgTe6V0EffLmd7ah7/aZJFzVem6OLTSqlS0wuqlUxGVi5fbktmyJ4NXP/ZJ3DypHWDLmWnlCoF7blXMrPWHyTVw5sH5RC8+ioMGaJztiulSk177pVITp6Fz1cm0KNFXbq9/rX1xXHjnBuUUsolac+9MoiKgqFDmf/TCo6kZvJgv5bOjkgp5eKqZ3K3JdNKc6EyIoI/difzwvpkrjibRP9Te5wdkVLKxVXPskxEBCxebH0cGYkxhkVbE/l8URyPxPzMwAn3VOjydZ/+cyKvbj1D57SjfPrtc7jFX60XUJVSZWLPMnveIrJORDaLyDYRiSimzZMisl1E4kTkTxFpXj7hOkh4OPTsCSkprFuwgls/XMPD328g7kQWTwQP4OBr79p3HAf8BbA0/jivbDvLDV0a8cPojjToc7VeQFVKlZk9ZZksYKAx5kqgKzBURHoVarMRCDXGdAHmAG86NkwHCwtjTY363NniZm5flUZiUipvjurC74PrYjw9ebzPWHLyLMXvWzCh5/8FEFHk884u2bkWXl6wnZaBtXjvjm74XNtbF71WSjlEicndWKXbnnravkyhNkuNMWdsT9cCTRwapYMlJKXzrx7/4kCdhjy77EuWRn/I7aFNaTH4Gl6/K4yNyXm8/Xt88TsXTOjh4fYPVSyml//OV0tJSMrgxd/ep8Y1vSvPNQCllMuzq+ZuWxw7FmgNTDPGRF+i+Vhg0UWOMw4YB9CsWbPSRVpGK35dwbeRmzkZ0pYDOW541fDgl+9fon5dX5j62bl2w7s0Ys2eZnyyPIFeLesxoF39Cw+Un8jDw609bHtq41FRcNNNpKZn4k8EREayNP44n+zOZMyG3xiw7Gdru4gIrbUrpRxCjDElt8pvLBIA/Aw8ZozZWsz2McCjQD9jTNaljhUaGmpiYmJKGW4pRUWROeU/vHnrBL5IyKLR6SRayVkCGgYyevYH9Hl0TLHjyDNz8rhl2mqOp2WxaPy1NKjtfVnvfa53HxHBwn3pPHzLJEY1rUHPnu15fdFOgtzz+GXBf/BOTQY/P5g6VUsySqlLEpFYY0xoie1Kk9xtBw4HMowxbxd6fRDwAdbEfryk41REct834g4eDLyWnfVbcE8LLyb9MhXvyS/ADTdAair4+0NKSrH77j6ezk0frKJLE39mPNALdze5IGHn9ujJKwt30Mjfm3F9WxU9wNCh1vLNkCGkTnqR6+Ydxs3XlxNZBgvQ/OwpPh/egtbXX1Ou3wOlVNVib3IvsSwjIkFAjjEmRUR8gEHAG4XadAM+AYbak9jLnS0JR4Q9wJE0+KKnLwNv7Qf/b5B1e+PG1uTeuPFFD9G6vi8v39KJp2dv5v0/d/HPXs147cs1DN+dTL8RtzD+xW9ZeCTn4sm9QPnm9aO+nKqRwrxxfajxyEOcjY6hS+IuJH4IXK9lGKWU45XYcxeRLsDXgDvWC7A/GmOmiMgUIMYYM09E/gA6A0dtux0wxoy41HHLtec+dChJK6Pp9eg3jBvQhmeHtr9we8GSSQllkCd/2MTPmw7TroEfOxPTLtjWtWkAmw6mEP3v6y5aulmy/RgPfBPDA9e24PnhHazvPWGCdaOWYZRSpVRuZRlHcXRyN8bw9hd/0fn3uQwZeCVPxZ7m57pXsOTJvrSu73fZx83IyuWmN5eQkGHh5S41STxrYdquTCZ3qknXvl0Z+eEa3hrVhdtCm2KxGLYfPc32o6fZeTSNDQeSiTuUQofg2sx5sDfenrqiklKqbBxWlnEVs2MOMW1XJrWC+7NzzRbmNurJE0ejab2nLtS//N5xLS8Pvlr/Jev2nuQfmzyRyEjGZmRTt1YNLBZDuwZ+fLx8D/+4qglPffgHPx/KBsDb042Owf482tabu356F+9QD+2lK6UqTJXouR9KPsPQ91bSyscQfyqTTDdPrkk7wNcfPYr79YPLPrywYBkHLijpzN98hMdmbuSeFl58vTeLu2MXcE/NZEJ+nmm9CJt/YbVePZg/XxO8UqpMqk3P3WIxTJwThzGG/43ry/K/k5i57gDvdemC+57BjrmVv+B49l69IDraOspm7VqGdW7E1CV/8/XeDIJPH2dS3K/4/PITRK+1fgiMHAkxMdZFN3Qcu1Kqgrh8cv8mah9r9pzk9ZGdaVq3JmN6NWdML9vUNv3LP5G6uwlPDG7L4zM38sLJGGtiDws732MHa4+9YM9fKaXKmUsn94SkdF6P3En/dkHccXXTinnTqVMvTNRRUYyYMIF+Ht74v/Xa+bLL5dzJqpRSDuKyNfc8i2HUx2tISMrg9wl9zw9FLMUwR4co2EMfMkSTuFKqXFX5mvv0FQlsPJDCf+/seuEY80JztZe78PDzd7lq2UUpVUm4ZHLfuXglU/9M5obG3oy4MvjCjQXLIRUhLAzWrq2Y91JKKTu55DJ7n85ciVf2Wf4z53VE5MKN+fVtHXKolKrGXDK5H/GqTejhHdTLOVNyY6WUqoZcMrnPvLc7H6Wvt45cUUopVYRL1twJC8N70W/OjkIppSotl+y5K6WUujRN7kopVQVpcldKqSqoxOQuIt4isk5ENovINhGJKKaNl4j8ICK7RSRaRELKI1illFL2safnngUMNMZcCXQFhopIr0JtxgLJxpjWwFQKLcOnlFKqYpWY3I1Vuu2pp+2r8IQ0N2Ndig9gDnCdFLm7SCmlVEWxq+YuIu4isgk4DiwxxkQXatIYOAhgjMkFUoF6jgxUKaWU/exK7saYPGNMV6AJ0ENEOhVqUlwvvch0kyIyTkRiRCQmKSmp9NEqpZSyS6luYjLGpIjIMmAosLXApkNAU+CQiHgA/sCpYvafDkwHEJEkEdlv51sHAidKE2sVoeddvVTH866O5wxlO+/m9jQqMbmLSBCQY0vsPsAgil4wnQfcA0QBo4C/TAkTxRtjguwJ0BZDjD3zF1c1et7VS3U87+p4zlAx521Pz70R8LWIuGMt4/xojFkgIlOAGGPMPOBz4FsR2Y21x35nuUWslFKqRCUmd2NMHNCtmNcnF3icCdzm2NCUUkpdLle5Q3W6swNwEj3v6qU6nnd1PGeogPN22hqqSimlyo+r9NyVUkqVQqVK7iIyVETibXPUPFfM9io5h40d5/2kiGwXkTgR+VNE7BoKVdmVdN4F2o0SESMiLj+qwp5zFpHbbT/vbSIyo6JjLA92/I43E5GlIrLR9ns+zBlxOpKIfCEix0Vk60W2i4i8b/uexInIVQ4NwBhTKb4Ad2AP0BKoAWwGOhRq8zDwse3xncAPzo67gs57AFDT9vih6nLetnZ+wApgLRDq7Lgr4GfdBtgI1LE9r+/suCvovKcDD9kedwD2OTtuB5x3X+AqYOtFtg8DFmG9CbQXEO3I969MPfcewG5jTIIxJhuYhXXOmoKq4hw2JZ63MWapMSZ/wdi1WO8UdnX2/LwBXgbeBDIrMrhyYs85PwBMM8YkAxhjjldwjOXBnvM2QG3bY3/gSAXGVy6MMSso5mbOAm4GvjFWa4EAEWnkqPevTMn93Pw0NodsrxXbxlSdOWzsOe+CxmL9tHd1JZ63iHQDmhpjFlRkYOXInp91W6CtiKwWkbUiMrTCois/9pz3S8AYETkELAQeq5jQnKq0//dLpTKtoWrP/DR2zWHjYuw+JxEZA4QC/co1oopxyfMWETes00ffW1EBVQB7ftYeWEsz/bH+hbZSRDoZY1LKObbyZM95jwa+Msa8IyJhWG+K7GSMsZR/eE5TrvmsMvXc8+enydeEon+anWtzqTlsXIw9542IDAKeB0YYY7IqKLbyVNJ5+wGdgGUisg9rTXKei19Utfd3/FdjTI4xZi8QjzXZuzJ7znss8COAMSYK8MY6/0pVZtf//ctVmZL7eqCNiLQQkRpYL5jOK9Qmfw4bsHMOGxdQ4nnbyhOfYE3sVaEGCyWctzEm1RgTaIwJMcaEYL3WMMIYE+OccB3Cnt/xX7BeQEdEArGWaRIqNErHs+e8DwDXAYjIFViTe1WfOnYecLdt1EwvINUYc9RhR3f2FeVirh7/jfXK+vO216Zg/U8N1h/4bGA3sA5o6eyYK+i8/wCOAZtsX/OcHXNFnHehtstw8dEydv6sBXgX2A5sAe50dswVdN4dgNVYR9JsAq53dswOOOeZwFEgB2svfSzwIPBggZ/1NNv3ZIujf7/1DlWllKqCKlNZRimllINocldKqSpIk7tSSlVBmtyVUqoK0uSulFJVkCZ3pZSqgjS5K6VUFaTJXSmlqqD/DytLYNqfouhlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x153fa343eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "showLwlrPlot(xMat, yMat, 0.003)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 小例子---预测鲍鱼年龄"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rssError(yMat,yHat):\n",
    "    '''误差和'''\n",
    "    return ((np.array(yMat)-np.array(yHat))**2).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "abXMat, abYMat = loadDataSet('abalone.txt')\n",
    "xMat = abXMat[0:99]\n",
    "yMat = abYMat[0:99]\n",
    "yHat01 = lwlrTest(xMat, xMat, yMat, 0.1)\n",
    "yHat1 = lwlrTest(xMat, xMat, yMat, 1)\n",
    "yHat10 = lwlrTest(xMat, xMat, yMat, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "56.78420911837208\n",
      "429.89056187030394\n",
      "549.1181708826065\n"
     ]
    }
   ],
   "source": [
    "print(rssError(yMat, yHat01))\n",
    "print(rssError(yMat, yHat1))\n",
    "print(rssError(yMat, yHat10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25119.459111157415\n",
      "573.5261441895706\n",
      "517.5711905381745\n"
     ]
    }
   ],
   "source": [
    "yHat01 = lwlrTest(abXMat[100:199], xMat, yMat, 0.1)\n",
    "print(rssError(abYMat[100:199], yHat01))\n",
    "yHat1 = lwlrTest(abXMat[100:199], xMat, yMat, 1)\n",
    "print(rssError(abYMat[100:199], yHat1))\n",
    "yHat10 = lwlrTest(abXMat[100:199], xMat, yMat, 10)\n",
    "print(rssError(abYMat[100:199], yHat10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "518.6363153250693\n"
     ]
    }
   ],
   "source": [
    "ws = standRegres(xMat, yMat)\n",
    "yHat = abXMat[100:199] * ws\n",
    "print(rssError(abYMat[100:199], yHat))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 岭回归（ridge regression）\n",
    "当数据的特征比样本还多时，矩阵x为非满秩矩阵，求逆会出现问题<br/>\n",
    "**岭回归**是对使用 $ (X^TX + \\lambda I) $ 从而使得矩阵非奇异，来求逆, $ I_(m \\times m) $ 的单位矩阵<br/>\n",
    "参数求解： $$ w = (X^TX + \\lambda I)^{-1}X^Ty $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ridgeRegres(xMat,yMat,lam=0.2):\n",
    "    xTx = xMat.T*xMat\n",
    "    denom = xTx + np.eye(np.shape(xMat)[1])*lam\n",
    "    if np.linalg.det(denom) == 0.0:\n",
    "        print(\"This matrix is singular, cannot do inverse\")\n",
    "        return\n",
    "    ws = denom.I * (xMat.T*yMat)\n",
    "    return ws\n",
    "    \n",
    "def ridgeTest(xMat,yMat):\n",
    "    yMean = np.mean(yMat,axis=0)\n",
    "    yMat = yMat - yMean     #to eliminate X0 take mean off of Y\n",
    "    #regularize X's\n",
    "    xMeans = np.mean(xMat,axis=0)   #calc mean then subtract it off\n",
    "    xVar = np.var(xMat,axis=0)      #calc variance of Xi then divide by it\n",
    "    xMat = (xMat - xMeans)/xVar\n",
    "    numTestPts = 30\n",
    "    wMat = np.zeros((numTestPts,np.shape(xMat)[1]))\n",
    "    for i in range(numTestPts):\n",
    "        ws = ridgeRegres(xMat,yMat,np.exp(i-10))\n",
    "        wMat[i,:]=ws.T\n",
    "    return wMat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "abXMat, abYMat = loadDataSet('abalone.txt')\n",
    "ridgeWeights = ridgeTest(abXMat, abYMat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24a4bfcf080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(ridgeWeights)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regularize(xMat):#regularize by columns\n",
    "    inMat = xMat.copy()\n",
    "    inMeans = np.mean(inMat,axis=0)   #calc mean then subtract it off\n",
    "    inVar = np.var(inMat,axis=0)      #calc variance of Xi then divide by it\n",
    "    inMat = (inMat - inMeans)/inVar\n",
    "    return inMat\n",
    "\n",
    "def stageWise(xMat,yMat,eps=0.01,numIt=100):\n",
    "    yMean = np.mean(yMat,axis=0)\n",
    "    yMat = yMat - yMean     #can also regularize ys but will get smaller coef\n",
    "    xMat = regularize(xMat)\n",
    "    m,n=np.shape(xMat)\n",
    "    returnMat = np.zeros((numIt,n)) #testing code remove\n",
    "    ws = np.zeros((n,1)); wsTest = ws.copy(); wsMax = ws.copy()\n",
    "    for i in range(numIt):\n",
    "        print(ws.T)\n",
    "        lowestError = np.inf; \n",
    "        for j in range(n):\n",
    "            for sign in [-1,1]:\n",
    "                wsTest = ws.copy()\n",
    "                wsTest[j] += eps*sign\n",
    "                yTest = xMat*wsTest\n",
    "                rssE = rssError(yMat.A,yTest.A)\n",
    "                if rssE < lowestError:\n",
    "                    lowestError = rssE\n",
    "                    wsMax = wsTest\n",
    "        ws = wsMax.copy()\n",
    "        returnMat[i,:]=ws.T\n",
    "    return returnMat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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    {
     "data": {
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       "array([[ 0.  ,  0.  ,  0.  , ...,  0.  ,  0.  ,  0.  ],\n",
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       "       [ 0.  ,  0.  ,  0.  , ...,  0.  ,  0.  ,  0.  ],\n",
       "       ...,\n",
       "       [ 0.05,  0.  ,  0.09, ..., -0.64,  0.  ,  0.36],\n",
       "       [ 0.04,  0.  ,  0.09, ..., -0.64,  0.  ,  0.36],\n",
       "       [ 0.05,  0.  ,  0.09, ..., -0.64,  0.  ,  0.36]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xMat, yMat = loadDataSet('abalone.txt')\n",
    "stageWise(xMat, yMat, 0.01, 200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "[[ 0.043 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
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      "[[ 0.043 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.044 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
      "[[ 0.043 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n",
      "[[ 0.044 -0.011  0.12   0.022  2.023 -0.963 -0.105  0.187]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.   ,  0.   ,  0.   , ...,  0.   ,  0.   ,  0.   ],\n",
       "       [ 0.   ,  0.   ,  0.   , ...,  0.   ,  0.   ,  0.   ],\n",
       "       [ 0.   ,  0.   ,  0.   , ...,  0.   ,  0.   ,  0.   ],\n",
       "       ...,\n",
       "       [ 0.043, -0.011,  0.12 , ..., -0.963, -0.105,  0.187],\n",
       "       [ 0.044, -0.011,  0.12 , ..., -0.963, -0.105,  0.187],\n",
       "       [ 0.043, -0.011,  0.12 , ..., -0.963, -0.105,  0.187]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stageWise(xMat, yMat, 0.001, 5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 0.0430442 , -0.02274163,  0.13214087,  0.02075182,  2.22403814,\n",
       "         -0.99895312, -0.11725427,  0.16622915]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xMat = regularize(xMat)\n",
    "yM = np.mean(yMat, 0)\n",
    "yMat = yMat - yM\n",
    "weights = standRegres(xMat, yMat)\n",
    "weights.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.045  0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n",
      "[[ 0.04   0.     0.105  0.025  1.295 -0.83  -0.06   0.26 ]]\n"
     ]
    }
   ],
   "source": [
    "returnMat = stageWise(xMat, yMat, 0.005, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24a4de79978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(returnMat)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
